Optimal control and cost-effectiveness analysis of age-structured malaria model with asymptomatic carrier and temperature variability

Abstract

This paper presents an age-structured mathematical model for malaria transmission dynamics with asymptomatic carrier and temperature variability. The temperature variability function is fitted to the temperature data, and the malaria model is then fitted to the malaria cases and validated to check its suitability. Time-dependent controls were considered, including Long Lasting Insecticide Nets, treatment of symptomatic, screening and treatment of asymptomatic carriers and spray of insecticides. Pontryagin's Maximum Principle is used to derive the necessary conditions for optimal control of the disease. The numerical simulations of the optimal control problem reveal that the strategy involving the combination of all four controls is the most effective in reducing the number of infected individuals. Furthermore, the cost-effectiveness analysis shows that treatment of symptomatic, screening and treatment of asymptomatic carriers and insecticide spraying is the most cost-effective strategy to implement to control malaria transmission when available resources are limited.

Keywords:

• Age structure
• malaria
• asymptomatic carrier
• temperature
• optimal control
• cost-effectiveness

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

‘This work was funded by a grant from the African Institute for Mathematical Sciences, www.nexteinstein.org, with financial support from the Government of Canada, provided through Global Affairs Canada, www.international.gc.ca, and the International Development Research Centre, www.idrc.ca’. Also, the corresponding author acknowledges with gratitude the Ministry of Education, Science and Technology – Tanzania for financial support.